The invention relates to the field of simulation and calculation of crack propagation in given structures and particularly for crack propagation simulation under cyclical loading of a structure. The invention can be used for all computer-supported design processes and is especially suitable for designing highly loaded and/or safety-critical components, for example, in aircraft or engine construction. Cyclical loading occurs in this context especially during takeoff and landing of the aircraft.
In the article xe2x80x9cCutting of a 3-D finite element mesh for automatic mode I crack propagation calculationsxe2x80x9d by Guido Dhondt, published in International Journal for Numerical Methods in Engineering, volume 42 (1998), pp. 749-772, a method for crack propagation simulation is disclosed. In this method, it is assumed that the crack propagates in a plane. Even though this assumption is useful for many applications, it generally limits the accuracy of the simulation.
An object of the invention is to provide a method for crack propagation simulation that can be used in many fields of application and operates with an accuracy as high as possible. Preferably, the method should not require too much calculating time, so that the simulations can be performed for many load cycles within a realistic time frame.
According to the invention, this object is achieved by a method comprising the steps of:
a) providing a defined three-dimensional structure and an initial crack therein;
b) calculating a cut through the structure in propagation of the initial crack;
c) determining a new crack front, by evaluating stress values by a finite element calculation and by using a crack propagation function;
d) triangulating a propagated crack along the new crack front; and
e) repeating the steps b) through e) until a predetermined end condition is fulfilled.
The invention is based on the basic concept of establishing crack shapes which extend not necessarily in a plane but follow instead any curved surface shape. The crack shape is generated during the course of the method as a triangulated surface and is updated. According to the invention, it is thus possible to calculate cracks of a complex shape with high accuracy. This provides computer-supported design methods that are considerably more efficient and versatile. The otherwise required high expenditure for practical experiments can be reduced while a high reliability of the designed components is obtained.
According to the invention, it is provided to triangulate the propagated crack whose new crack front has been determined by a finite element calculation and application of a crack propagation function. This includes the alternatives that the entire crack calculated up to this point is newly triangulated or that the triangulation of the present crack is maintained and only the crack increment added by the actual iteration process is newly triangulated. In each iteration process, the propagation which is generated at the beginning of the iteration serves only for internal purposes and has little or no effect on the result of the simulation.
In preferred embodiments of the invention, a crack propagation is first generated for calculating the cut structure. This can be done, for example, in that first the outer contour of the crack is supplemented with additional triangles to a convex crack contour and, subsequently, further triangles are added until the crack propagation penetrates the entire structure. In a further step at least each element of the structure cut by the crack propagation can be divided into at least two parts so that the crack propagation extends always along the boundary surfaces and not through individual parts. Preferably, in yet another step it is provided by further dividing elements of the structure that the crack front extends along the boundaries (edges) of structural elements.
In order to achieve with acceptable calculating expenditure a crack propagation simulation for as many cycles of a cyclical loading as possible, in preferred embodiments multiple load cycles are simulated during one iteration, (i.e., on the basis of a single finite element calculation of stress values). Accordingly, the crack propagation over, for example, 100 or 200 cycles is calculated and, only subsequent thereto, the entire crack increment obtained over the course of this cycle is triangulated and used as the initial crack for the next iteration.
Preferably, the number of simulated cycles is determined such that the crack propagation just reaches or just exceeds at least at one point along the crack front a predetermined maximum value (for example, 50 xcexcm). This calculation can be achieved by an inner loop in which the crack propagation is successively added until the maximum value of the crack propagation is reached. In an especially simple embodiment, however, the result of a single application of the crack propagation function is scaled such that the maximum value just reaches the predetermined limit.